Oscillation criteria for selfadjoint differential systems
Author:
William T. Reid
Journal:
Trans. Amer. Math. Soc. 101 (1961), 91106
MSC:
Primary 34.30
MathSciNet review:
0133518
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References 
Similar Articles 
Additional Information
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 [1]
 N. I. Achieser and I. M. Glasmann, Theorie der linearen Operatoren im HilbertRaum, AkademieVerlag, Berlin, 1954. MR 0066560 (16:596f)
 [2]
 J. H. Barrett, Twopoint boundary value problems and comparison theorems for fourthorder selfadjoint differential equations and secondorder matrix differential equations, Technical Summary Report #150, April, 1960, Mathematics Research Center, U. S. Army.
 [3]
 G. D. Birkhoff and M. R. Hestenes, Natural isoperimetric conditions in the calculus of variations, Duke Math. J. vol. 1 (1935) pp. 198286. MR 1545876
 [4]
 G. A. Bliss, Lectures on the calculus of variations, University of Chicago Press, 1946. MR 0017881 (8:212e)
 [5]
 M. Bôcher, Applications and generalizations of the concept of adjoint systems, Trans. Amer. Math. Soc. vol. 14 (1913) pp. 403420. MR 1500954
 [6]
 M. R. Hestenes, Applications of the theory of quadratic forms in Hilbert space to the calculus of variations, Pacific J. Math. vol. 1 (1951) pp. 525581. MR 0046590 (13:759a)
 [7]
 H. C. Howard, Oscillation criteria for fourthorder linear differential equations, Trans. Amer. Math. Soc. vol. 96 (1960) pp. 296311. MR 0117379 (22:8159)
 [8]
 K. S. Hu, The problem of Bolza and its accessory boundary value problem (Dissertation, University of Chicago, 1932), Contributions to the Calculus of Variations, University of Chicago Press, 19311932, pp. 361443.
 [9]
 W. Leighton, The detection of the oscillation of solutions of a second order linear differential equation, Duke Math. J. vol. 17 (1950) pp. 5762. MR 0032065 (11:248c)
 [10]
 W. Leighton and Z. Nehari, On the oscillation of solutions of selfadjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. vol. 89 (1958) pp. 325377. MR 0102639 (21:1429)
 [11]
 M. Morse, Sufficient conditions in the problem of Lagrange with fixed end points, Ann. of Math. vol. 32 (1931) pp. 567577. MR 1503017
 [12]
 , Sufficient conditions in the problem of Lagrange with variable end conditions, Amer. J. Math. vol. 53 (1931) pp. 517546. MR 1507924
 [13]
 , The calculus of variations in the large, Amer. Math. Soc. Colloquium Publications, vol. 18, 1934.
 [14]
 Z. Nehari, Oscillation criteria for secondorder linear differential equations, Trans. Amer. Math. Soc. vol. 85 (1957) pp. 428445. MR 0087816 (19:415a)
 [15]
 W. T. Reid, A boundary value problem associated with the calculus of variations, Amer. J. Math. vol. 54 (1932) pp. 769790. MR 1506937
 [16]
 , An integrodifferential boundary value problem, Amer. J. Math. vol. 60 (1938) pp. 257292. MR 1507311
 [17]
 , A matrix differential equation of Riccati type, Amer. J. Math. vol. 68 (1946) pp. 237246; also Addendum, ibid., vol. 70 (1948) p. 460. MR 0015610 (7:446a)
 [18]
 , Oscillation criteria for linear differential systems with complex coefficients, Pacific J. Math. vol. 6 (1956) pp. 733751. MR 0084655 (18:898a)
 [19]
 , Adjoint linear differential operators, Trans. Amer. Math. Soc. vol. 85 (1957) pp. 446461. MR 0088625 (19:550d)
 [20]
 , Principal solutions of nonoscillatory selfadjoint linear differential equations, Pacific J. Math. vol. 8 (1958) pp. 147169. MR 0098220 (20:4682)
 [21]
 H. M. Sternberg and R. L. Sternberg, A twopoint boundary problem for ordinary selfadjoint differential equations of fourth order, Canad. J. Math. vol. 6 (1954) pp. 416419. MR 0061738 (15:874c)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719610133518X
PII:
S 00029947(1961)0133518X
Article copyright:
© Copyright 1961
American Mathematical Society
